Question

The area enclosed by the curves $x^2=y,y=x+2$ and x-axis is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$
• D. $\frac{5}{6}$

Answer 1

The correct option is D $\frac{5}{6}$

Required Area is given by
${\int }_{-2}^{-1}(x+2)dx+{\int }_{-1}^0{x}^{2}dx$
$=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}$.